Such a radiation source is known from DE-OS 37 16 618 which corresponds to U.S. Pat. No. 4,903,287. The disclosed metal screen serves to keep (scattered) electrons remote from the target, which would lead to polychromatic stray radiation being produced in the target besides the substantially monochromatic fluorescence radiation. This screen is traversed by the X-ray radiation emitted by the anode and converted in the target into fluorescence radiation. In order to avoid that the screen absorbs an excessive quantity of X-ray radiation and on the other hand itself emits due to scattered or secondary electrons (polychromatic) X-ray radiation, the screen is as thin-walled as possible and consists of a low-atomic material (for example titanium (with a target of tantalum)).